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Representations Subduced on an Ideal of a Lie Algebra

Published online by Cambridge University Press:  20 November 2018

B. Noonan
B. Noonan*
Affiliation:
Summer Research Institute Canadian Mathematical Congress
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This paper considers the properties of the representation of a Lie algebra when restricted to an ideal, the subduced* representation of the ideal. This point of view leads to new forms for irreducible representations of Lie algebras, once the concept of matrices of invariance is developed. This concept permits us to show that irreducible representations of a Lie algebra, over an algebraically closed field, can be expressed as a Lie-Kronecker product whose factors are associated with the representation subduced on an ideal. Conversely, if one has such factors, it is shown that they can be put together to give an irreducible representation of the Lie algebra. A valuable guide to this work was supplied by a paper of Clifford (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 293 - 303
Copyright
Copyright © Canadian Mathematical Society 1962

References

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